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Find the lengths of chords of the circum...

Find the lengths of chords of the circumcircle of triangle ABC, made by its altitudes

Text Solution

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From the figure, in `Delta ABL`,
`angleABL = angleABD + angleDBL`
`= B + (90^(@) - C)`
`90^(@) + (B -C)`
`AL = x`
using sine rule in `DeltaABL`, we get `(x)/(sin (90^(@) + B - C)) = 2R`
`x = 2R cos (B -C)`
Similarly, `y = 2R cos (C -A)`
`z = 2R cos (A -B)`
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